Abstract
This paper investigates geometric and ontological aspects of shape concepts underlying the semantics of nouns. Considering the German shape nouns Ecke and Knick (corner and kink) we offer a geometric framework to characterize substantial aspects of shape based on features of the object’s boundary. Using the axiomatic method, we develop a geometric system, called ‘planar shape geometry’, enriching the basic inventory of ordering geometry by shape curves. The geometric characterization is not sufficient to decide which are the referents of the nouns Ecke and Knick among the entities involved in the spatial constellation. Different tests using the German topological prepositions in and an (in and at) are employed to bring forth this decision for the case of Ecke. Since these tests do not give uniform evidence in favor of one solution, we have to conclude that Ecke is flexible in selecting the referent and the characterizations discussed reflect its meaning spectrum.
The research reported in this paper has been supported by the Deutsche Forschungsgemeinschaft (DFG) in the project ‘Axiomatik räumlicher Konzepte’ (Ha 1237/7). We are indebted to Christie Manning, Bernhard Nebel, Esther Rinke, Christoph Schlieder, Hedda Rahel Schmidtke, Mark Siebel, and Heike Tappe for their helpful comments. This paper also benefits from the fruitful discussions in the Hamburg Working Group on Spatial Cognition.
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References
Biederman, I. (1987). Recognition-by-components: A theory of human image understanding. Psychological Review, 94, 115–147.
Biederman, I. (1995). Visual object recognition. In S.M. Kosslyn & D.N. Osherson (eds.), Visual Cognition—An Invitation to Cognitive Science (2nd ed.) Vol. 2. (pp. 121–165). Cambridge, MA: MIT.
Bierwisch, M. (1983). Semantische und konzeptuelle Repräsentation lexikalischer Einheiten. In W. Motsch & R. Ruzicka (eds.), Untersuchungen zur Semantik. (pp. 61–99). Berlin: Akademie-Verlag.
Bierwisch, M. (1988). On the grammar of local prepositions. In M. Bierwisch, W. Motsch & I. Zimmermann (eds.), Syntax, Semantik und Lexikon. (pp. 1–63). Berlin: Akademie-Verlag.
Bierwisch, M. (1996). How much space gets into language? In P. Bloom, M.A. Peterson, L. Nadel & M.F. Garrett (eds.), (pp. 31–76).
Bierwisch, M. & Lang, E. (1989). Somewhat longer—much deeper—further and further. In M. Bierwisch & E. Lang (eds.), Dimensional Adjectives: Grammatical Structure and Conceptual Interpretation. (pp. 471–514). Berlin, Heidelberg, New York: Springer.
Buschbeck-Wolff, B. (1994). Konzeptuelle Interpretation und interlinguabasierte Übersetzung räumlicher Präpositionen (Working Papers of the Institute for Logic and Linguistics, IBM TR-80.95-015). Stuttgart: IBM.
Bloom, P., Peterson, M.A., Nadel, L. & Garrett, M.F. (eds.) (1996). Language and Space. Cambridge, MA: MIT.
Eilan, N., McCarthy, R. & Brewer, B. (eds.) (1993). Spatial Representations. Oxford: Blackwell.
Eisenkolb, A., Musto, A., Schill, K. Hernández, D. & Brauer, W. (1998). Representational Levels for the Perception of the Courses of Motion. This volume.
Eschenbach, C. & Kulik, L. (1997). An axiomatic approach to the spatial relations underlying left-right and in front of-behind. In G. Brewka, C. Habel & B. Nebel (eds.), KI-97—Advances in Artificial Intelligence. (pp. 207–218). Berlin: Springer.
Habel, Ch. (1990). Propositional and depictorial representations of spatial knowledge: The case of path concepts. In R. Studer (ed.), Natural Language and Logic. (pp. 94–117). Berlin: Springer.
Habel, Ch. & Eschenbach, C. (1997). Abstract structures in spatial cognition. In C. Freksa, M. Jantzen & R. Valk (eds.), Foundations of Computer Science. Potential-Theory-Cognition. (pp. 369–378). Berlin: Springer.
Henkin, L., Suppes, P. & Tarski, A. (eds.) (1959): The Axiomatic Method, with Special Reference to Geometry and Physics. Amsterdam: North-Holland.
Herskovits, A. (1986). Language and Spatial Cognition. Cambridge, Eng.: Cambridge University Press.
Herweg, M. (1989). Ansätze zu einer semantischen Beschreibung topologischer Präpositionen. In Ch. Habel, M. Herweg & K. Rehkämper (eds.), Raumkonzepte in Verstehensprozessen. (pp. 99–127). Tübingen: Niemeyer.
Hilbert, D. (1899). Grundlagen der Geometrie. (8th ed. (1956), with revisions and additions by Paul Bernays.) Stuttgart: Teubner.
Hoffman, D.D. & Richards, W.A. (1984). Parts of recognition. Cognition, 18, 65–97.
Hoffman, D.D. & Singh, M. (1997). Salience of visual parts. Cognition, 63, 29–78.
Huntington, E.V. (1924). A new set of postulates for betweenness, with proof of complete independence. Transactions of the American Mathematical Society, 26, 257–282.
Jackendoff, R. (1991). Parts and boundaries. Cognition, 41, 9–45.
Jackendoff, R. (1996). The architecture of the linguistic-spatial interface. In P. Bloom, M.A. Peterson, L. Nadel & M.F. Garrett (eds.), (pp. 1–30).
Klein, W. (1991). Raumausdrücke. Linguistische Berichte, 132, 77–114.
Kline, M. (1972). Mathematical Thought—From Ancient to Modern Times. New York: Oxford University Press.
Knauff, M., Rauh, R., Schlieder, Ch.. & Strube, G. (1998). Mental Models in Spatial Reasoning. This volume.
Laguna, T. de (1922). Point, line and surface, as sets of solids. The Journal of Philosophy, 19, 449–461.
Landau, B. & Jackendoff, R. (1993). “What” and “where” in spatial language and spatial cognition. Behavioral and Brain Sciences, 16, 217–238.
Landau, B., Leyton, M., Lynch, E. & Moore, C. (1992). Rigidity, malleability, object kind, and object naming. Paper presented at the Psychonomics Society, St. Louis, MO.
Landau, B., Smith, L., & Jones, S. (1988). The importance of shape in early lexical learning. Cognitive Development, 3, 299–321.
Lang, E. (1989). The semantics of dimensional designation of spatial objects. In M. Bierwisch & E. Lang (eds.), Dimensional Adjectives: Grammatical Structure and Conceptual Interpretation. (pp. 263–417). Berlin, Heidelberg, New York: Springer.
Luce, R.D., Krantz, D.H., Suppes, P. & Tversky, A. (1990). Foundations of Measurement. Vol. III. Representation, Axiomatization and Invariance. San Diego, CA: Academic Press.
Mandler, J. M. (1996). Preverbal representation and language. In P. Bloom, M.A. Peterson, L. Nadel & M.F. Garrett (eds.), (pp. 365–384).
Marr, D. & Nishihara, H.K. (1978). Representation and recognition of the spatial organization of three-dimensional shape. In Proc. of the Royal Society, Series B, 200. (pp. 269–294).
Miller, G.A. (1978). Semantic relations among words. In M. Halle, J. Bresnan & G. Miller (eds.), Linguistic Theory and Psychological Reality. (pp. 60–117). Cam., MA: MIT.
Miller, G.A. & Johnson-Laird, P. (1976). Language and Perception. Cam., MA: Belknap.
Parchomenko, A.S. (1957). Was ist eine Kurve? Berlin: Deutscher Verlag der Wissenschaften.
Peterson, M.A., Nadel, L., Bloom, P. & M.F. Garrett (1996). Space and language. In P. Bloom, M.A. Peterson, L. Nadel & M.F. Garrett (eds.), (pp. 553–577).
Pinkal, M. (1985). Logik und Lexikon: Die Semantik des Unbestimmten. Berlin: de Gruyter.
Pinker, S. (1984). Visual cognition: An introduction. Cognition, 18, 1–63.
Pribbenow, S. (1993). Räumliche Konzepte in Wissens-und Sprachverarbeitung—Hybride Verarbeitung von Lokalisierung. Wiesbaden: Deutscher Universitäts-Verlag.
Renz, J. & Nebel, B. (1998). Spatial Reasoning with Topological Information. This Volume.
Rosch, E., Mervis, C., Gray, W., Johnson, D. & Boyes Braem, P. (1976). Basic objects in natural categories. Cognitive Psychology, 8, 382–439.
Smith, E.E. (1995). Concepts and categorization. In E.E. Smith & D.H. Osherson (eds.), Thinking. An Invitation to Cognitive Science (2nd ed.) Vol. 3. (pp. 3–33). Cambridge, MA: MIT.
Vieu, L. (1993). A logical framework for reasoning about space. In A.U. Frank & I. Campari (eds.), Spatial Information Theory. A Theoretical Basis for GIS. (pp. 25–35). Berlin: Springer.
Wunderlich, D. & Herweg, M. (1991). Lokale und Direktionale. In A. von Stechow & D. Wunderlich (eds.), Semantik. (pp. 758–785). Berlin, New York: de Gruyter.
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Eschenbach, C., Habel, C., Kulik, L., Leßmöllmann, A. (1998). Shape Nouns and Shape Concepts: A Geometry for ‘Corner’. In: Freksa, C., Habel, C., Wender, K.F. (eds) Spatial Cognition. Lecture Notes in Computer Science(), vol 1404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69342-4_9
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